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QuestionA geneticist has 473 green and 164 yellow beans. Estimate the probability of a green offspring bean as a percent. Round to one decimal place. Is it close to 34\frac{3}{4}? yes or no.

Studdy Solution

STEP 1

Assumptions1. The total number of beans is the sum of green beans and yellow beans. . The probability of getting an offspring bean that is green is the ratio of green beans to the total number of beans.

STEP 2

First, we need to find the total number of beans. We can do this by adding the number of green beans and yellow beans.
Total beans=Green beans+Yellow beansTotal\, beans = Green\, beans + Yellow\, beans

STEP 3

Now, plug in the given values for the number of green beans and yellow beans to calculate the total number of beans.
Total beans=473+164Total\, beans =473 +164

STEP 4

Calculate the total number of beans.
Total beans=473+164=637Total\, beans =473 +164 =637

STEP 5

Now that we have the total number of beans, we can find the probability of getting a green bean. This is the ratio of green beans to the total number of beans.
Probability of green=Green beansTotal beansProbability\, of\, green = \frac{Green\, beans}{Total\, beans}

STEP 6

Plug in the values for the number of green beans and the total number of beans to calculate the probability.
Probability of green=473637Probability\, of\, green = \frac{473}{637}

STEP 7

Calculate the probability of getting a green bean.
Probability of green=473637≈0.7422Probability\, of\, green = \frac{473}{637} \approx0.7422

STEP 8

To report the answer as a percent rounded to one decimal place, we multiply the probability by100 and round to one decimal place.
Probability of green (in percent)=Probability of green×100Probability\, of\, green\, (in\, percent) = Probability\, of\, green \times100

STEP 9

Plug in the value for the probability of green to calculate the probability in percent.
Probability of green (in percent)=.7422×100Probability\, of\, green\, (in\, percent) =.7422 \times100

STEP 10

Calculate the probability of getting a green bean in percent.
Probability of green (in percent)=0.7422×100=74.2%Probability\, of\, green\, (in\, percent) =0.7422 \times100 =74.2\%The estimated probability of getting an offspring bean that is green is74.2%.

STEP 11

Now, we need to determine if this result is reasonably close to the expected value of 34\frac{3}{4} or0.75. We can do this by comparing the calculated probability of0.742 with0.75.
If ∣0.742−0.75∣≤0.01|0.742 -0.75| \leq0.01, we can consider the result as reasonably close to the expected value.

STEP 12

Calculate the absolute difference between the calculated probability and the expected value.
∣0.7422−0.75∣=0.0078|0.7422 -0.75| =0.0078Since0.0078 is less than or equal to0.01, we can consider the result as reasonably close to the expected value. So, the answer is "yes".

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